{
  "id": "1003.1349",
  "version": "v1",
  "published": "2010-03-06T03:52:17.000Z",
  "updated": "2010-03-06T03:52:17.000Z",
  "title": "The minimal sequence of Reidemister moves bringing the diagram of $(n+1,n)$-torus knot to that of $(n,n+1)$-torus knot",
  "authors": [
    "Chuichiro Hayashi",
    "Miwa Hayashi"
  ],
  "comment": "10pages, 17 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "Let $D(p,q)$ be the usual knot diagram of the $(p,q)$-torus knot, that is, $D(p,q)$ is the closure of the $p$-braid $(\\sigma_1^{-1} \\sigma_2^{-1}... \\sigma_{p-1}^{-1})^q$. As is well-known, $D(p,q)$ and $D(q,p)$ represent the same knot. It is shown that $D(n+1,n)$ can be deformed to $D(n,n+1)$ by a sequence of $\\{(n-1)n(2n-1)/6 \\} + 1$ Reidemeister moves, which consists of a single RI move and $(n-1)n(2n-1)/6$ RIII moves. Using cowrithe, we show that this sequence is minimal over all sequences which bring $D(n+1,n)$ to $D(n,n+1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-06T03:52:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25"
    ],
    "keywords": [
      "torus knot",
      "reidemister moves bringing",
      "minimal sequence",
      "single ri move",
      "usual knot diagram"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1349H"
    }
  }
}